Strategy is concerned with sustained interfirm profitability differences. Observations of such sustained differencesare often attributed to unobserved systematic a priori differences in firm characteristics. This papershows that sustained interfirm profitability differences may be very likely even if there are no a priori differencesamong firms. As a result of the phenomenon of long leads in random walks, even a random resourceaccumulation process is likely to produce persistent resource heterogeneity and sustained interfirm profitabilitydifferences. A Cournot model in which costs follow a random walk shows that such a process could produceevidence of substantial persistence of profitability. The results suggest that persistent profitability doesnot necessarily provide strong evidence for systematic a priori differences among firms. Nevertheless, since thephenomenon of long leads is highly unrepresentative of intuitive notions of random sequences, such evidencemay still be persuasive.